Figures REF  and REF  show us that the statistical utility when plotted against the loss parameter denoting the maximum average distortion, for each the two location datasets, results in producing a Pareto curve. We see that the EMD between the true and the estimated PMFs for a fixed number of cycles of Optima3 run with a given number of iterations for BA and IBU, such that the entire method numerically converges, prominently decreases and becomes stable as \(\beta \)  increases, i.e., the amount of locally injected noise decreases. This depicts an improvement of the estimated PMF until it advances to converge to the true PMF with an increase of the loss parameter. This observation is consistent with the Pareto-behaviour of mutual information with the maximum average distortion as studied in rate-distortion theory [1]}, and thus, we empirically bridge together the two ends of utility we focused on in this paper.
